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Let $G$ be a simple n$n$-vertex graph and let $\mu_n\geq\mu_{n-1}\geq\dots\geq\mu_1$ be the eigenvalues of its Laplacian matrix, how can I find a function $$f(\mu_1,\mu_2,\dots\mu_n) \text{ such that } e(G)= f(\mu_1,\mu_2,\dots\mu_n)?$$
Let $G$ be a simple n-vertex graph and let $\mu_n\geq\mu_{n-1}\geq\dots\geq\mu_1$ be the eigenvalues of its Laplacian matrix, how can I find a function $$f(\mu_1,\mu_2,\dots\mu_n) \text{ such that } e(G)= f(\mu_1,\mu_2,\dots\mu_n)?$$
Let $G$ be a simple $n$-vertex graph and let $\mu_n\geq\mu_{n-1}\geq\dots\geq\mu_1$ be the eigenvalues of its Laplacian matrix, how can I find a function $$f(\mu_1,\mu_2,\dots\mu_n) \text{ such that } e(G)= f(\mu_1,\mu_2,\dots\mu_n)?$$
Let $G$ be a simple n-vertex graph and let $\mu_n\geq\mu_{n-1}\geq\dots\geq\mu_1$ be the eigenvalues of its Laplacian matrix, how can I find a function $$f(\mu_1,\mu_2,\dots\mu_n) \text{ such that } e(G)= f(\mu_1,\mu_2,\dots\mu_n)?$$
